Curves projected on object
I'm not sure you need a curve at all. Here's how I would go about a model like this.
First I would make a &quot;sphere&quot; by adding a subdivision surface to a cube with three subdivision levels (CTRL+3). I would then add a cast modifier and cast it as a sphere, to make the mesh a true sphere shape.

Then I would apply the modifiers, and make the egg shape using proportional editing set to smooth.

Then I would inset THESE faces, and scale them inwards slightly.

I would also scale the &quot;seam&quot; edges closer together on their respective axes:

Then I would turn proportional editing back on, but set to random this time, making sure to check &quot;connected only&quot;. I would then select some random vertices along the edges of the &quot;petal seams&quot; and scale them towards each other on whatever axis they lie. (I know the &quot;gaps&quot; are wider in the first image - I took this screenshot early, before I scaled the edges).


Do this for all the &quot;seams&quot;, then select the centre areas again, and inset by a small amount.

Do the same for the outer areas - this helps define the edges of the &quot;petals&quot;

You should then be able to select the whole surround edge as one loop - you can then extrude this (extrude faces along normals) to form the lip.

Lastly,  add another subdivision surface modifier, and shade smooth to smooth it out.

Hope this helps.